Correction of Cross-Component Induction Measurements for Misalignment Using Comparison of the XY Formation Response

ABSTRACT

Measurements are made with a multicomponent logging tool in an earth formation. The measurements are inverted without using a selected cross-component measurement. The model is then used to predict the value of the selected cross-component. A misalignment angle of the tool is estimated from the predicted and actual values of the selected cross-component.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.11/400,536, by Rabinovich et al., filed Apr. 6, 2006 which is related toU.S. patent application Ser. No. 11/398,838 to Rabinovich et al., filedApr. 6, 2006 and U.S. patent application Ser. No. 11/400,097 toRabinovich et al., filed Apr. 6, 2006.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is related to the field of apparatus design in thefield of oil exploration. In particular, the present invention describesa method for calibrating multicomponent logging devices used fordetecting the presence of oil in boreholes penetrating a geologicalformation.

2. Description of the Related Art

Electromagnetic induction resistivity well logging instruments are wellknown in the art. Electromagnetic induction resistivity well logginginstruments are used to determine the electrical conductivity, and itsconverse, resistivity, of earth formations penetrated by a borehole.Formation conductivity has been determined based on results of measuringthe magnetic field of eddy currents that the instrument induces in theformation adjoining the borehole. The electrical conductivity is usedfor, among other reasons, inferring the fluid content of the earthformations. Typically, lower conductivity (higher resistivity) isassociated with hydrocarbon-bearing earth formations. The physicalprinciples of electromagnetic induction well logging are well described,for example, in, J. H. Moran and K. S. Kunz, Basic Theory of InductionLogging and Application to Study of Two-Coil Sondes, Geophysics, vol.27, No. 6, part 1, pp. 829-858, Society of Exploration Geophysicists,December 1962. Many improvements and modifications to electromagneticinduction resistivity instruments described in the Moran and Kunzreference, supra, have been devised, some of which are described, forexample, in U.S. Pat. No. 4,837,517 to Barber, in U.S. Pat. No.5,157,605 to Chandler et al., and in U.S. Pat. No. 5,600,246 to Faniniet al.

The conventional geophysical induction resistivity well logging tool isa probe suitable for lowering into the borehole and it comprises asensor section containing a transmitter antenna and a receiver antennaand other, primarily electrical, equipment for measuring data to inferthe physical parameters that characterize the formation. The sensorsection, or mandrel, comprises induction transmitters and receiverspositioned along the instrument axis, arranged in the order according toparticular instrument or tool specifications and oriented parallel withthe borehole axis. The electrical equipment generates an electricalvoltage to be further applied to a transmitter induction coil,conditions signals coming from receiver induction coils, processes theacquired information, stores the data or, by means of telemetry sendsthe data to the earth surface through a wire line cable used to lowerthe tool into the borehole.

In general, when using a conventional induction logging tool withtransmitters and receivers (induction coils) oriented only along theborehole axis, the hydrocarbon-bearing zones are difficult to detectwhen they occur in multi-layered or laminated reservoirs. Thesereservoirs usually consist of thin alternating layers of shale and sandand, oftentimes, the layers are so thin that due to the insufficientresolution of the conventional logging tool they cannot be detectedindividually. In this case the average conductivity of the formation isevaluated.

Conventional induction well logging techniques employ coils wound on aninsulating mandrel. One or more transmitter coils are energized by analternating current. The oscillating magnetic field produced by thisarrangement results in the induction of currents in the formations thatare nearly proportional to the conductivity of the formations. Thesecurrents, in turn, contribute to the voltage induced in one or morereceiver coils. By selecting only the voltage component that is in phasewith the transmitter current, a signal is obtained that is approximatelyproportional to the formation conductivity. In conventional inductionlogging apparatus, the basic transmitter coil and receiver coil haveaxes that are aligned with the longitudinal axis of the well loggingdevice. (For simplicity of explanation, it will be assumed that the borehole axis is aligned with the axis of the logging device, and that theseare both in the vertical direction. Also single coils will subsequentlybe referred to without regard for focusing coils or the like.) Thisarrangement tends to induce secondary current loops in the formationsthat are concentric with the vertically oriented transmitting andreceiving coils. The resultant conductivity measurements are indicativeof the horizontal conductivity (or resistivity) of the surroundingformations. There are, however, various formations encountered in welllogging which have a conductivity that is anisotropic. Anisotropyresults from the manner in which formation beds were deposited bynature. For example, “uniaxial anisotropy” is characterized by adifference between the horizontal conductivity, in a plane parallel tothe bedding plane, and the vertical conductivity, in a directionperpendicular to the bedding plane. When there is no bedding dip,horizontal resistivity can be considered to be in the planeperpendicular to the bore hole, and the vertical resistivity in thedirection parallel to the bore hole. Conventional induction loggingdevices, which tend to be sensitive only to the horizontal conductivityof the formations, do not provide a measure of vertical conductivity orof anisotropy. Techniques have been developed to determine formationanisotropy. See, e.g. U.S. Pat. No. 4,302,722 to Gianzero et al..Transverse anisotropy often occurs such that variations in resistivityoccur in the azimuthal direction.

Thus, in a vertical borehole, a conventional induction logging tool withtransmitters and receivers (induction coils) oriented only along theborehole axis responds to the average horizontal conductivity thatcombines the conductivity of both sand and shale. These average readingsare usually dominated by the relatively higher conductivity of the shalelayers and exhibit reduced sensitivity to the lower conductivity sandlayers where hydrocarbon reserves are produced. To address this problem,loggers have turned to using transverse induction logging tools havingmagnetic transmitters and receivers (induction coils) orientedtransversely with respect to the tool longitudinal axis. Suchinstruments for transverse induction well logging have been described inPCT Patent publication WO 98/00733 of Beard et al. and U.S. Pat. No.5,452,761 to Beard et al.; U.S. Pat. No. 5,999,883 to Gupta et al.; andU.S. Pat. No. 5,781,436 to Forgang et al.

One, if not the main, difficulty in interpreting the data acquired by atransversal induction logging tool is associated with vulnerability ofits response to borehole conditions. Among these conditions is thepresence of a conductive well fluid as well as wellbore fluid invasioneffects.

In the induction logging instruments, the acquired data quality dependson the formation electromagnetic parameter distribution (conductivity)in which the tool induction receivers operate. Thus, in the ideal case,the logging tool measures magnetic signals induced by eddy currentsflowing in the formation. Variations in the magnitude and phase of theeddy currents occurring in response to variations in the formationconductivity are reflected as respective variations in the outputvoltage of receivers. In the conventional induction instruments, thesereceiver induction coil voltages are conditioned and then processedusing analog phase sensitive detectors or digitized by digital-to-analogconverters and then processed with signal processing algorithms. Theprocessing allows for determining both receiver voltage amplitude andphase with respect to the induction transmitter current or magneticfield waveform. It has been found convenient for further upholegeophysical interpretation to deliver the processed receiver signal as avector combination of two voltage components: one being in-phase withtransmitter waveform and another out-of-phase, quadrature component.Theoretically, the in-phase coil voltage component amplitude is the moresensitive and noise-free indicator of the formation conductivity.

Recognizing the fact that no hardware calibration is perfect, and mayfurther be susceptible to changes over time, the present inventionprovides methods for calibration of multicomponent induction logginginstruments in the presence of possible hardware errors andmisalignments.

SUMMARY OF THE INVENTION

One embodiment of the invention is a method of estimating a parameter ofinterest of an earth formation. A logging tool is conveyed into aborehole in the earth formation. Multi-component measurementsresistivity measurements are obtained using the logging tool. Themulti-component measurements are inverted without using a particularcross-component to give a resistivity model. The resistivity model isused to provide a simulated value of the particular cross-component. Thesimulated value and the actual value of the particular cross-componentare used for estimating a misalignment angle in the logging tool.

Another embodiment of the invention is an apparatus for estimating aparameter of interest of an earth formation. A logging tool obtains aplurality of multi-component resistivity measurements. A processorinverts the multi-component measurements while excluding a particularcross-component to give a resistivity model. The processor then uses theresistivity model to provide a simulated value of the particularcross-component. The processor than uses the simulated value and theactual value of the particular cross-component to estimate amisalignment angle in the logging tool.

Another embodiment of the invention is a computer readable medium foruse with an apparatus for estimating a parameter of interest of an earthformation. The apparatus includes a logging tool which obtains aplurality of multi-component resistivity measurements. The instructionsenable a processor to invert the multi-component measurements whileexcluding a particular cross-component to give a resistivity model. Theinstructions further enable the processor to use the resistivity modelto provide a simulated value of the particular cross-component. Theinstructions then enable the processor to use the simulated value andthe actual value of the particular cross-component to estimate amisalignment angle in the logging tool.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is best understood with reference to theaccompanying figures in which like numerals refer to like elements andin which:

FIG. 1 shows schematically a wellbore extending into a laminated earthformation, into which wellbore an induction logging tool as usedaccording to the invention has been lowered;

FIG. 2A (prior art) illustrates a conventional resistivity measurementin the vertical direction;

FIG. 2B (prior art) illustrates a resistivity measurement in thehorizontal direction;

FIG. 3 shows a borehole inclined to a bedding plane;

FIG. 4 shows a flow chart of one embodiment of the present inventionusing quadrature signals;

FIG. 5 shows a flow chart of another embodiment of the present inventionusing average signals; and

FIG. 6 shows a flow chart of an embodiment of the present inventionusing inversion.

DETAILED DESCRIPTION OF THE INVENTION

The instrument structure provided by the present invention enablesincreased stability and accuracy in an induction wellbore logging tooland its operational capabilities, which, in turn, results in betterquality and utility of wellbore data acquired during logging. Thefeatures of the present invention are applicable to improve the accuracyof a transverse induction tool.

The invention will now be described in more detail, and by way ofexample, with reference to the accompanying drawings. FIG. 1schematically shows a wellbore 1 extending into a laminated earthformation, into which wellbore an induction logging tool 9 as usedaccording to the present invention has been lowered. The wellbore inFIG. 1 extends into an earth formation that includes ahydrocarbon-bearing sand layer 3 located between an upper shale layer 5and a lower shale layer 7, both having higher conductivity than thehydrocarbon bearing sand layer 3. An induction logging tool 9 used inthe practice of the invention has been lowered into the wellbore 1 via awireline 11 extending through a blowout preventor 13 (shownschematically) located at the earth surface 15. The surface equipment 22includes an electric power supply to provide electric power to the setof coils 18 and a signal processor to receive and process electricsignals from the receiver coils 19. Alternatively, the power supplyand/or signal processors are located in the logging tool. It is to benoted that the term “coil” is intended to include antennas made ofnon-circular conductors as well as conductor arrangements (includingrectangular configurations) limited to a plane that are commonly used totransmit and receive electromagnetic energy.

The relative orientation of the wellbore 1 and the logging tool 9 withrespect to the layers 3, 5, 7 is determined by two angles, one of whichθ as shown in the FIG. 1. For determination of these angles see, forexample, U.S. Pat. No. 5,999,883 to Gupta, et al. The logging tool 9 isprovided with a set of transmitter coils 18 and a set of receiver coils19, each set of coils 18, 19 being connected to surface equipment 22 viasuitable conductors (not shown) extending along the wireline 11.

Each set of coils 18 and 19 includes three coils (not shown), which arearranged such that the set has three magnetic dipole moments in mutuallyorthogonal directions, that is, in x, y and z directions. The three-coiltransmitter coil set transmits T_(x), T_(y) and T_(z). The receiver coilreceives R_(x), R_(y) and R_(z) plus the cross-components, R_(xy),R_(xz) and R_(zy). Thus, coil set 18 has magnetic dipole moments 26 a,26 b, 26 c, and coil set 19 has magnetic dipole moments 28 a, 28 b, 28c. In one embodiment, the transmitter coil set 18 is electricallyisolated from the receiver coil set 19 The apparatus and method using awireline is not intended to be a limitation of the invention, it beingpossible to practice the invention with a logging tool on a bottomholeassembly (BHA) conveyed on a drilling tubular. For the purposes of thepresent invention, the BHA and the assembly described in FIG. 1 may bereferred to as a downhole assembly.

As shown in FIG. 2A, conventional induction logging tools provide asingle transmitter coil and a receiver coil that measure resistivity inthe horizontal direction. In the conventional horizontal mode, as shownin FIG. 2A, the resistivities of adjacent high resistivity sand and lowresistivity shale layers appear in parallel, thus the resistivitymeasurement is dominated by low resistivity shale. As shown in FIGS. 1and 2B, in the present invention a transverse coil is added to measureresistivity in the vertical direction. In the vertical direction, theresistivity of the highly resistive sand and low resistivity shale areappear in series and thus the vertical series resistivity measurement isdominated by the resistivity of the highly resistive sand.

For ease of reference, normal operation of the tool 9, as shown in FIGS.1 and 2B, will be described hereinafter only for the coils having dipolemoments in the x-direction, i.e. dipole moments 26 a and 28 a. Duringnormal operation an alternating current of a frequency f₁ is supplied bythe electric power supply of surface equipment 22 to transmitter coilset 18 so that a magnetic field with magnetic dipole moment 26 a isinduced in the formation. In an alternative embodiment, the frequency isswept through a range f₁ through f₂. This magnetic field extends intothe sand layer 3 and induces a number of local eddy currents in the sandlayer 3. The magnitude of the local eddy currents is dependent upontheir location relative to the transmitter coil set 18, the conductivityof the earth formation at each location, and the frequency at which thetransmitter coil set 18 is operating. In principle, the local eddycurrents act as a source inducing new currents, which again inducefurther new currents, and so on. The currents induced into the sandlayer 3 induce a response magnetic field in the formation, whichresponse magnetic field is not in phase with the transmitted magneticfield, but which induces a response current in receiver coil set 19. Themagnitude of the current induced in the sand layer 3 depends on theconductivity of the sand layer 3 and affects the magnitude of theresponse current in receiver coil set 19. The magnitude of the responsecurrent in receiver coil 19 also depends on the conductivity of sandlayer 3 and thereby provides an indication of the conductivity of thesand layer 3. However, the magnetic field generated by transmitter coilset 18 not only extends into sand layer 3, but also into the wellborefluid and into the shale layers 5 and 7 so that currents in the wellborefluid and the shale layers 5 and 7 are induced.

Let us consider H_(XY) measurement, where X is orientation of thetransmitter and Y is the orientation of the receiver. This notationwhere the first subscript refers to the transmitter orientation and thesecond to the receiver orientation will be used throughout the presentdisclosure. We assume that if the coils are properly aligned (exactly90° between X and Y coils) the response from the formation will beH_(XYtrue). If the Y receiver is misaligned with the X transmitter bythe angle α, then the magnetic field H_(XY) measured in such array isH _(XY) =H _(XYtrue)·cos α+H _(XXtrue)·sin α  (1).The angle α is considered to be positive if the angle between the X andY coils is less than 90°. Those skilled in the art having the benefit ofthe present disclosure would recognize that the misalignment angle couldchange over time for wireline measurements and MWD applications.

A simple example shows that even when the misalignment angle α is small(typically 1-5°) there are quite a few cases where the misalignmenterror becomes comparable with the true Hxy response. In the example,R_(h), the horizontal resistivity in a direction normal to theanisotropy axis is taken as 0.5 Ω-.m; R_(v), the vertical resistivity(in a direction parallel to the anisotropy axis) is taken as 2 Ω-.m; therelative dip angle θ (see FIG. 3) between the tool axis and theanisotropy axis is 20°. For a relative toolface rotation of 45° and afrequency of 83.3 kHz, the true response (real voltage converted toapparent conductivities) for the XX component is −524.3 mS/m and for theXY component is 25.4 mS/m.

For a misalignment angle of 3°, the measured XY signal will beσ_(XYmeasured)=25.4 mS/m·cos 3°−524.3 mS/m·sin 3°=−2.1 mS/mWe can see that in this case the misalignment error exceeds 100%, havingchanged by an amount of about 27.5 mS/m. If the misalignment angle α isknown, Eqn. 1 can be used for correcting the measured XY signal.Unfortunately, the misalignment angle α cannot be measured in advancebecause it can change during pre-logging tool string assembly and alsowhile logging due to twisting and bending effects.

In one embodiment of the invention, the misalignment angle α isestimated and the measurements are corrected using a multi-frequencyquadrature signal. The 3DEX tool has a 3-coil configurations (twotransmitter and one receiver coils) for cross-components that are notmutually balanced. The main reason for mutually balanced multi-coilarrays in induction measurements (including main components of the 3DEXtool) is compensation of the direct field in quadrature components. Thisdirect field is large compared to the formation response, so if it isnot compensated and the phase detection is not accurate enough, it willpropagate in the real voltage and cause undesired distortion. Forcross-components measurements, the mutual balancing is not as importantbecause the direct field of the X transmitter does not contribute intothe Y receiver due to orthogonality. But if the X and Y coils aremisaligned, the direct field from unbalanced X transmitters doescontribute to the Y quadrature signal. The misalignment angle α isestimated based on the amplitude of this signal.

Eqn. (1) is used to analyze the misaligned XY quadrature signal. Theresponse consists of the cosine projection of true XY formationquadrature signal and the sine projection of true XX signal. The true XXsignal is dominated by the direct field, which is frequency andformation independent. If we extract the constant part of the XYquadrature signal and compare it with the total direct field, we will beable to find the misalignment angle. For example, let us consider the3DEX response in the following model:

-   R_(h)=1 Ω-m;-   R_(v)=4 Ω-m;-   Relative dip=45°;-   Relative rotation=45°;-   Frequency=20.83 kHz.

The values of the XY quadrature formation response and the direct fieldfor a 2° misalignment for this model are presented in Table 1. It can beseen that in this case the formation response is comparable with thedirect field, meaning that we have to separate the direct field from theformation response to accurately estimate the misalignment angle. TABLE1 Comparison of the XY formation response and the direct field caused by2° misalignment Direct field for 2° XY formation response misalignmentFormation relative Re(Hxy) (Wb/m²) (Wb/m²) contribution % 0.0474 * 10⁻³−0.0903 * 10⁻³ 52.5

The separation of the direct field from the formation response in thequadrature signal may be achieved by applying the Taylor expansion usedin multi-frequency focusing of the real signal. Using results from U.S.Pat. No. 5,884,227 to Rabinovich et al., the quadrature signal is givenby the Taylor series expansion:Re(H)=b ₀ +b ₁ω^(3/2) +b ₂ω² +b ₃ω^(5/2) +b ₄ω^(7/2) +b ₅ω⁴ +b₆ω^(9/2)  (2)The first term in this expansion is independent of frequency andrepresents the direct field. In the present invention, multi-frequencyquadrature measurements are made and this first term is extracted usingthe Taylor series expansion. Typically, this is done using amulti-frequency focusing algorithm with the appropriate power series. Totest our invention, we generated synthetic data for two differentmodels:

-   1. R_(h)=10 Ω-m; R_(v)=40 Ω-m, Relative dip=45°, Relative    rotation=45°;-   2. R_(h)=1 Ω-m; R_(v)=4 Ω-m, Relative dip=45°, Relative    rotation=45°.

For each model we calculated responses for 5 different misalignmentangles: 0, 1, 2, 3, 4, 5 degrees. The term “misalignment angle” whenused with respect to coils that are nominally orthogonal to each othermeans a difference from 90° in alignment. For each misalignment angle weapplied the above-described procedure to extract the direct field fromthe data, and based on this value, calculated the misalignment angle.The results for the both models are presented in the tables below. TABLE2 Calculation of the misalignment angle for the Model 1. True Extracteddirect Calculated misalignment field Total direct field misalignmentangle angle (deg) (Wb/m²) (Wb/m²) (deg) 5 −0.225 * 10⁻³ −0.2586 * 10⁻²4.99 4 −0.180 * 10⁻³ −0.2586 * 10⁻² 3.99 3 −0.135 * 10⁻³ −0.2586 * 10⁻²2.99 2 −0.902 * 10⁻⁴ −0.2586 * 10⁻² 1.999 1 −0.451 * 10⁻⁴ −0.2586 * 10⁻²0.999 0 −0.450 * 10⁻⁶ −0.2586 * 10⁻² 0.01

TABLE 3 Calculation of the misalignment angle for the Model 2. TrueExtracted direct Calculated misalignment field Total direct fieldmisalignment angle angle (deg) (Wb/m²) (Wb/m²) (deg) 5 −0.224 * 10⁻³−0.2586 * 10⁻² 4.97 4 −0.179 * 10⁻³ −0.2586 * 10⁻² 3.97 3 −0.134 * 10⁻³−0.2586 * 10⁻² 2.97 2 −0.885 * 10⁻⁴ −0.2586 * 10⁻² 1.96 1 −0.433 * 10⁻⁴−0.2586 * 10⁻² 0.96 0 −0.188 * 10⁻⁵ −0.2586 * 10⁻² 0.04

This embodiment of the invention may be represented by the flow chart ofFIG. 4. Data are acquired at a plurality of frequencies 101. As aspecific example, the transmitter is an X transmitter and the receiveris a Y receiver. A multi-frequency focusing of the quadrature magneticsignal is performed 103 using eqn. (2) to give the direct field betweenthe transmitter and the receiver. This may also be done using anequivalent formulation for the electric field using methods known tothose versed in the art having the benefit of the present disclosure.Using the estimated direct field, the misalignment angle is estimated105. The estimated misalignment angle may then be used to correct theindividual single frequency measurements, including the in-phasecomponents 107. It should be noted that while the description above hasbeen made with respect to the XY component, from reciprocityconsiderations, the method is equally valid for the YX component.

Once the misalignment angle is estimated, all of the multi-componentsignals can be corrected for misalignment and used for interpretingformation resistivities and petrophysical parameters. The principlesused for this interpretation have been discussed, for example, in U.S.Pat. No. 6,470,274 to Mollison et al, U.S. Pat. No. 6,643,589 to Zhanget al., U.S. Pat. No. 6,636,045 to Tabarovsky et al., the contents ofwhich are incorporated herein by reference. Specifically, the parametersestimated may include horizontal and vertical resistivities (orconductivities), relative dip angles, strike angles, sand and shalecontent, and water saturation.

The method described above is generally not applicable when a co-locatedtransmitter coil array is used in conjunction with a co-located mainreceiver coil array and a co-located bucking receiver coil array. Insuch a situation, the main and bucking coils are decoupled and themisalignment is estimated separately for the main and bucking coils.

A second embodiment of the invention is based on recognition of the factthat for a given anisotropic formation with a particular relative dip,the XY cross-component response will change from a negative value at−45° relative rotation to a positive value of equal magnitude at 45°relative rotation. A zero-crossing will occur at 0° relative rotation.The actual magnitude of the positive and negative values will bedependent on the resistivity and the relative dip properties of theformation, but the response should always oscillate about zero for aperfectly aligned tool rotating in a uniform anisotropic formation.

If the X transmitters and the Y receiver are misaligned, a portion ofthe direct XX signal will be introduced into the XY response asdescribed previously. If the tool is rotating through a uniformformation, the deviation of the oscillations away from zero allows thismisalignment to be computed.

To apply the technique, a relatively uniform formation (typically athick shale interval) is chosen for making measurements with the 3DEXtool. The tool is rotated within the borehole. For wirelineapplications, this may require an auxiliary motor for rotating the toolor may result from rotation of the wireline and the downhole assembly asit is conveyed through the borehole. For measurement-while-drilling(MWD) applications, the rotation is accomplished by the rotation of thebottomhole assembly (BHA) that carries the 3DEX tool. The average XY andXX responses across this formation are computed. Based on the eqn. (1)and the assumption that the average H _(XYtrue) should be zero, wherethe overbar represents an averaging, the misalignment angle may becomputed using average responses.H _(XY) =H _(XXtrue)·sin α  (3)This technique assumes that the misalignment is not changing and willnot compensate for twisting and bending while logging unless the effectremains consistent. The estimation of bias in ZX measurements on arotating drillstring has been discussed in U.S. patent application Ser.No. 11/299,053 of Chemali et al, having the same assignee as the presentinvention and the contents of which are incorporated herein byreference. Once the misalignment angle has been estimated, measurementsmay be corrected using eqn. (1).

The flow chart for this method is illustrated in FIG. 5. The tool islowered into a substantially homogenous interval 201. The H_(xx) andH_(xy) measurements are made at a plurality of rotational angles as thetool rotates 203. The H_(xy) measurements correspond to measurementsmade with a first receiver antenna and the H_(xx) measurementscorresponds to measurements made with a second receiver antenna. Themeasurements are averaged and the misalignment angle estimated 205. Inone embodiment of the invention, the measurements are made at uniformlyspaced angles and a simple averaging can be done. In another embodimentof the invention, the measurements may be made with non-uniformrotational angles and an appropriate averaging procedure may be used.The estimated bias provides and estimate of the misalignment angle maythen be used to correct the measurements 207 made in other portions ofthe wellbore using eqn. (1) and a parameter of interest of the earthformation estimated.

Another embodiment of the present invention uses an inversion of 3DEXdata to obtain horizontal resistivity, vertical resistivity, andformation dip and azimuth, and requires the use of multi-componentmeasurements including the three primary components (XX,YY,ZZ) plus atleast one cross-component (XY or XZ). A method for simultaneousdetermination of formation angles and anisotropic resistivity usingmulti-component induction logging data is disclosed in U.S. Pat. No.6,643,589 to Zhang et al., having the same assignee as the presentinvention and the contents of which are incorporated herein byreference. The inversion is performed using a gradient technique such asa generalized Marquardt-Levenberg method. In this generalizedMarquardt-Levenberg method, a data objective function is defined that isrelated to a difference between the model output and the measured data.The iterative procedure involves reducing a global objective functionthat is the sum of the data objective function and a model objectivefunction related to changes in the model in successive iterations. In analternate embodiment of the invention, the formation azimuth angle isexcluded from the iterative process by using derived relations betweenthe multicomponent measurements. The gradient technique is part of aclass of techniques collectively referred to as search techniques.

When multi-array induction measurements are also available, an inversionmethod is described in U.S. Pat. No. 6,885,947 to Xiao et al., havingthe same assignee as the present invention and the contents of which areincorporated herein by reference. Data are acquired using a multi-arraylogging tool in a borehole having an angle of inclination to a normal tothe bedding plane of earth formations. The multi-array measurements arefiltered using angle dependent filters to give a filtered curvecorresponding to a target one of the multi-array measurements usingangle-dependent filters. Correlation coefficients are estimated for aset of possible dip angles and a relative dip angle is estimated fromthe correlation coefficients. This dip angle estimate together with bedboundaries obtained from the multi-array measurements are used forinverting multi-component measurements alone or jointly with multi-arraymeasurements to refine the relative dip angle interpretation and givehorizontal and vertical formation resistivity.

Yet another inversion method using a separation of modes is disclosed inU.S. Pat. No. 6,636,045 to Tabarovsky et al having the same assignee asthe present invention and the contents of which are incorporated hereinby reference. In Tabarovsky, a combination of principal componentmeasurements is used to estimate the horizontal resistivity of the earthformations. The estimated horizontal resistivities are used in a modelfor inversion of other components of the data to obtain the verticalformations resistivities. Tabarovsky further uses multifrequencyfocusing when multifrequency measurements are available.

Another inversion method is described in U.S. patent application Ser.No. 10/867,619 of Tabarovsky et al, having the same assignee as thepresent invention and the contents of which are incorporated herein byreference. In one embodiment of the Tabarovsky '619, using known valuesof the relative dip angle and azimuth, the focused measurements areseparated into two or more fundamental modes. One of the fundamentalmodes is related primarily to the horizontal conductivity (orresistivity) of the earth formation, so that the horizontal conductivitymay be obtained from the first mode. Using the estimated horizontalconductivity and the second mode, the vertical conductivity may beestimated. In another embodiment of the invention, the fundamental modesand the relative dip angle and azimuth are estimated simultaneouslyusing measurements made at a plurality of depths. The simultaneousdetermination is done by searching over a range of relative dip anglesand azimuths. Alternatively, the search may be done over a range ofabsolute dips and azimuths and using measurements made by orientationand navigation sensors on the tool.

One embodiment of the present invention uses an inversion technique suchas that described in Zhang et al., Xiao et al., Tabarovsky et al., orany other suitable inversion method. A common characteristic of all ofthe methods is that a more stable and unique solution for formation dipand azimuth is estimated when both cross-components are included.However, if the cross-components are perfectly aligned, the samesolution for formation dip and azimuth should be achieved if either theXY or the XZ components are omitted. If the XY component is in error dueto misalignment, this will not be true.

The inversion technique to check for misalignment initially inverts thedata with a particular cross-component such as the XY component omitted.Forward modeling is then used with these results to generate a simulated(expected) XY response. The average difference between the simulated andactual XY responses should be zero. Any difference is attributed tomisalignment.

To apply the technique, the average XX and XY responses are estimatedover the entire logging interval along with the average simulated XYresponse obtained by forward modeling from the inversion performedwithout the XY measurement. Based on the eqn. (1) and the assumptionthat the simulated XY response represents H_(XYtrue), the misalignmentangle may be computed using average responses.H _(xy) ^(measured) − H _(xy) ^(simulated) = H _(xx) sin αwhere the overbar represents and averaging. This technique also assumesthat the misalignment is not changing and will not compensate fortwisting and bending while logging unless the effect remains consistent.Once the correction is estimated and applied, a new inversion of themulti-component measurements may be carried out using all the availablecomponents.

FIG. 6 is a flow chart of this method. Multicomponent measurements(optionally with multiarray measurements) are acquired and themeasurements are inverted without using the XY component 301. SimulatedXY measurements are generated for the model 305. The XX and XYmeasurements are averaged over the interval 305. Next, the misalignmentangles is estimated 307 as discussed above.

Implicit in the control and processing of the data is the use of acomputer program on a suitable machine-readable medium that enables theprocessor to perform the control and processing. The machine-readablemedium may include ROMs, EPROMs, EAROMs, Flash Memories and Opticaldisks.

While the foregoing disclosure is directed to the preferred embodimentsof the invention, various modifications will be apparent to thoseskilled in the art. It is intended that all variations within the scopeand spirit of the appended claims be embraced by the foregoingdisclosure.

The following definitions are helpful in understanding the scope of theinvention:

-   alignment: the proper positioning or state of adjustment of parts in    relation to each other;-   calibrate: to standardize by determining the deviation from a    standard so as to ascertain the proper correction factors;-   coil: one or more turns, possibly circular or cylindrical, of a    current-carrying conductor capable of producing, a magnetic field;-   EAROM: electrically alterable ROM;-   EPROM: erasable programmable ROM;-   flash memory: a nonvolatile memory that is rewritable;-   machin-readable medium: something on which information may be stored    in a form that can be understood by a computer or a processor;-   misalignment: the condition of being out of line or improperly    adjusted; for the cross-component, this is measured by a deviation    from orthogonality;-   Optical disk: a disc-shaped medium in which optical methods are used    for storing and retrieving information;-   Position: an act of placing or arranging; the point or area occupied    by a physical object-   Quadrature: 90° out of phase; and-   ROM: Read-only memory.

1. A method of estimating a parameter of interest of an earth formation,the method comprising: (a) conveying a logging tool into a borehole inthe earth formation; (b) obtaining a plurality of multi-componentresistivity measurements using the logging tool; (c) inverting themulti-component resistivity measurements without using a particularcross-component to give a resistivity model; (d) using the resistivitymodel to provide a simulated value of the particular cross-component;and (e) using the simulated value of the particular cross-component andan actual value of the particular cross-component for estimating amisalignment angle in the logging tool.
 2. The method of claim 1 whereininverting the multi-component measurements further comprises using asearch technique.
 3. The method of claim 1 further comprising obtainingmulti-array induction measurements and using the multi-array inductionmeasurements in the inversion.
 4. The method of claim 1 whereininverting the multi-component measurements further comprises: (i) usinga first subset of the measurements to estimate a horizontal resistivityof the formation, and (ii) using the estimated horizontal resistivityand another subset of the measurements to estimate a verticalresistivity of the earth formation.
 5. The method of claim 1 whereininverting the multi-component measurements further comprises using aseparation of modes.
 6. The method of claim 1 wherein the particularcross-component is selected from (i) an XY component, and (ii) an XZcomponent.
 7. The method of claim 1 wherein determining the misalignmentangle further comprises using an average value of the particularcross-component and an average simulated value of the particularcross-component.
 8. The method of claim 1 further comprising using themisalignment angle and the multi-component measurements to estimate theparameter of interest of the earth formation.
 9. The method of claim 8wherein the parameter of interest is at least one of (i) a horizontalconductivity, (ii) a vertical conductivity, (iii) a horizontalresistivity, (iv) a vertical resistivity, (v) a relative dip angle, (vi)a strike angle, (vii) a sand fraction, (viii) a shale fraction, and (ix)a water saturation.
 10. An apparatus for estimating a parameter ofinterest of an earth formation, the apparatus comprising: (a) a loggingtool configured to be conveyed into a borehole in the earth formationand which is configured to obtain a plurality of multi-componentresistivity measurements; and (b) a processor which is configured to:(A) invert the multi-component resistivity measurements without using aparticular cross-component to give a resistivity model; (B) use theresistivity model to provide a simulated value of the particularcross-component; and (C) use the simulated value of the particularcross-component and an actual value of the particular cross-component toestimate a misalignment angle in the logging tool.
 11. The apparatus ofclaim 10 wherein the processor is configured to invert themulti-component measurements using a search technique.
 12. The apparatusof claim 10 wherein the processor is configured to invert themulti-component measurements using: (i) a first subset of themeasurements to estimate a horizontal resistivity of the formation, and(ii) the estimated horizontal resistivity and another subset of themeasurements to estimate a vertical resistivity of the earth formation.13. The apparatus of claim 10 wherein the processor is configured toinvert the multi-component measurements by using a separation of modes.14. The apparatus of claim 10 wherein the particular cross-component isselected from (i) an XY component, and (ii) an XZ component.
 15. Theapparatus of claim 10 wherein the processor is configured to estimatethe misalignment using an average value of the particularcross-component and an average simulated value of the particularcross-component.
 16. The apparatus of claim 10 wherein the processor isfurther configured to use the estimated misalignment angle and themulti-component measurements to estimate the parameter of interest ofthe earth formation.
 17. The apparatus of claim 16 wherein the parameterof interest is at least one of (i) a horizontal conductivity, (ii) avertical conductivity, (iii) a horizontal resistivity, (iv) a verticalresistivity, (v) a relative dip angle, (vi) a strike angle, (vii) a sandfraction, (viii) a shale fraction, and (ix) a water saturation.
 18. Theapparatus of claim 10 further comprising a wireline configured to conveythe logging tool into the borehole.
 19. The apparatus of claim 18further comprising a motor configured to rotate the logging tool to theplurality of rotational angles.
 20. The apparatus of claim 10 whereinthe logging tool is part of a bottomhole assembly (BHA) configured to beconveyed into the borehole on a drilling tubular.
 21. A computerreadable medium used with an apparatus for evaluating an earthformation, the apparatus comprising: (a) a logging tool configured to beconveyed into a borehole in the earth formation which is configured toobtain a plurality of multi-component resistivity measurements; themedium comprising instructions which enable a processor to (b) invertthe multi-component resistivity measurements without using a particularcross-component to give a resistivity model; (c) use the resistivitymodel to provide a simulated value of the particular cross-component;and (d) estimate a misalignment angle in the logging tool by using thesimulated value of the particular cross-component and an actual value ofthe particular cross-component.
 22. The medium of claim 20 furthercomprising at least one of (i) a ROM, (ii) an EPROM, (iii) an EAROMs,(iv) a flash memory, and (v) an Optical disk.